Systems and methods for locating buried or hidden objects using sheet current flow models

ABSTRACT

Systems, methods, and apparatus for determining an estimated depth of a buried object using sheet current flow models are disclosed. In one embodiment a buried object locator may process magnetic signals emitted from the buried object using a closed form sheet current flow model taken from three or more sensor positions to determine, store, and/or display estimated depth information of the buried object.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) to co-pendingU.S. Provisional Patent Application Ser. No. 61/531,598, filed Sep. 6,2011, entitled SYSTEMS & METHODS FOR LOCATING BURIED OR HIDDEN OBJECTSUSING SHEET CURRENT FLOW MODELS, the content of which is herebyincorporated by reference herein in its entirety for all purposes.

FIELD

The present disclosure relates generally to systems and methods forlocating buried or hidden objects. More particularly, but notexclusively, the disclosure relates to systems, methods, and apparatusfor locating buried objects using magnetic fields emitted from theobject and determining and displaying an estimate of the distance/depthof the object based on three or more magnetic field measurements takenat different positions relative to the buried object. The three or moremagnetic field measurements may be processed in accordance with a sheetcurrent flow model to determine the distance/depth estimate.

BACKGROUND

There are many situations where is it desirable to locate buriedutilities such as pipes and cables. For example, before starting any newconstruction that involves excavation, worker safety and projecteconomic concerns require the location and identification of existingunderground utilities such as underground power lines, gas lines, phonelines, fiber optic cable conduits, cable television (CATV) cables,sprinkler control wiring, water pipes, sewer pipes, etc., collectivelyand individually herein referred to as “buried objects.”

As used herein, the term “buried objects” also includes objects locatedinside walls, between floors in multi-story buildings or cast intoconcrete slabs, for example, as well as objects disposed below thesurface of the ground. If excavation equipment such as a backhoe hits ahigh voltage line or a gas line, serious injury and property damage mayresult. Unintended severing of water mains and sewer lines generallyleads to messy and expensive cleanup efforts. The unintended destructionof power and data cables may seriously disrupt the comfort andconvenience of residents and bring huge financial costs to business.Accordingly, the art is replete with proposed solutions to the buriedobject locating problem, including a number of patents and patentapplications owned by SeekTech, Inc., assignee of the instantapplication.

A sonde typically includes a coil of wire wrapped around a ferromagneticcore that is packaged for insertion into a buried nonconductive conduit,such as a plastic utility runway or a concrete water pipe to generateelectromagnetic energy. Still other buried objects, such as conductivelines and pipes, may be located by first applying an external signal tothe object to induce a current flow therein, thereby generating amagnetic field that may be detected by a magnetic sensor. In someapplications, currents may be induced into the buried object by existingmagnetic fields, such as those sent from commercial or military radiotransmitters or other transmitting devices.

In an exemplary buried object locating system, an external electricalsignal source (also known as a buried object transmitter or just“transmitter” for brevity) having a frequency in the range ofapproximately 4 Hz to 500 kHz has a well-known utility for energizingconductive objects by direct electrical coupling to permit theirlocation through sensing of emitted magnetic fields. Other buriedobjects, such as underground power transmission lines, inherently carrycurrent which generate surrounding magnetic fields. These examples ofactive and passive locating of buried conductors are also commonlydescribed as “line tracing.”

SUMMARY

This disclosure is directed generally to locators for use in detectingburied or hidden objects. More particularly, but not exclusively, thedisclosure relates to systems, methods, and apparatus for locatingburied objects using magnetic fields surrounding the object anddetermining the depth of the object based on three or more magneticfield measurements taken at different positions relative to the buriedobject using processing based on a sheet current flow model. Themagnetic field measurements may be taken by moving a single magneticfield sensor to multiple positions for taking measurements, and/or bytaking measurements from multiple magnetic field sensors offset a knownrelative distance from each other.

For example, in one aspect, the disclosure relates to a method forlocating a buried object with a buried object locator. The method mayinclude, for example, generating, in the locator, a first magnetic fieldmeasurement at a first position, generating, in the locator, a secondmagnetic field measurement at a second position different from the firstposition, generating, in the locator, a third magnetic field measurementat a third position different from the first and second positions, andstoring the first, second, and third magnetic field measurements andassociated position information in a memory of the locator. The methodmay further include processing, in a processing element of the locatoror other electronic computing system, the first, second, and thirdmagnetic field measurements and associated position information. Themeasurements and position information may be processed in accordancewith a closed-form sheet current flow model to generate an estimate ofthe depth, D_(b), of the buried object below a ground surface. Themethod may further include storing the estimated depth in the memory.The method may further include providing a visual display of theestimated depth on a display of the locator or other device. The methodmay further include sending the estimated depth to an externalelectronic computing system via a wired or wireless connection.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example, amagnetic field sensor assembly. The magnetic field sensor assembly mayinclude one or more magnetic field sensors configured to generate first,second, and third magnetic field measurement information atcorresponding first, second, and third positions, one or more memorymodules, and one or more processing modules coupled to the memory. Theprocessing modules may include one or more processing elementsconfigured to receive the first, second, and third magnetic fieldmeasurement information, process the received first, second, and thirdmagnetic field measurement information in accordance with a closed-formsheet current flow model to generate an estimated distance to the buriedobject, store the estimated depth in the memory, and provide a visualdisplay of the estimated depth on the locator.

In another aspect, the disclosure relates to a non-transitorymachine-readable medium containing processor-executable instructions forcausing a computer to receive first, second, and third magnetic fieldmeasurement information, and process the received first, second, andthird magnetic field measurement information in accordance with a sheetcurrent flow model to generate an estimated depth of a buried objectbelow a ground surface.

In another aspect, the disclosure relates to a method for locating aburied object with a buried object locator. The method may include, forexample, generating, in the locator, a lower magnetic field measurementat a first locator position, generating, in the locator, an uppermagnetic field measurement at the first locator position, generating, inthe locator, a lower magnetic field measurement at a second locatorposition different from the first position, generating, in the locator,an upper magnetic field measurement at the second locator position,storing the first and second locator position lower and upper magneticfield measurements in a memory of the locator, processing the first andsecond position lower and upper magnetic field measurements inaccordance with a closed-form sheet current flow model to generate anestimate of the depth, D_(b), of the buried object below a groundsurface, and storing the estimated depth in the memory. The estimate ofthe buried object depth, D_(b), may be determined using a closed-formsheet current flow model.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example, amagnetic field sensor assembly. The magnetic field sensor assembly mayinclude a plurality of magnetic field sensors configured to generatelower and upper magnetic field measurement information at first and asecond locator positions, a memory module, and a processor modulecoupled to the memory, wherein the processor is configured to processthe first and second position lower and upper magnetic fieldmeasurements in accordance with a closed-form sheet current flow modelto generate an estimate of the depth, D_(b), of the buried object belowa ground surface, store the estimated depth in the memory, and provide avisual display of the estimated depth on the locator. The estimateddepth, D_(b), may be determined in the processor module using aclosed-form sheet current flow model.

In another aspect, the disclosure relates to a non-transitorymachine-readable medium containing processor-executable instructions forcausing a computer to receive a lower magnetic field measurement at afirst locator position, an upper magnetic field measurement at the firstlocator position, a lower magnetic field measurement at a second locatorposition different from the first position, and an upper magnetic fieldmeasurement at the second locator position, store the first and secondlocator position lower and upper magnetic field measurements in amemory, and process the first and second position lower and uppermagnetic field measurements in accordance with a closed-form sheetcurrent flow model to generate an estimate of the depth of a buriedobject below a ground surface.

In another aspect, the disclosure relates to apparatus and systems forperforming the above-described methods, in whole or in part.

In another aspect, the disclosure relates to computer-readable mediaincluding instructions for causing a processor module or computer toperform the above-described methods, in whole or in part.

In another aspect, the disclosure relates to means for performing theabove-described methods, in whole or in part.

Various additional aspects, details, and functions are further describedbelow in conjunction with the appended drawing figures.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is nowmade to the following detailed description of the embodiments asillustrated in the accompanying drawings, in which like referencedesignations represent like features throughout the several views andwherein:

FIG. 1 illustrates details of an example buried object locationoperation (“line tracing”);

FIG. 2 illustrates details of example ground sub-surface features as maybe encountered during a line tracing operation;

FIG. 3 illustrates details of example conductor and ground current flowin a buried object locator system during a line tracing operation;

FIG. 4 illustrates details of one embodiment of a sheet current flowmodel for buried current flow in the ground;

FIG. 5 illustrates details of example conductor current magnetic fieldsand sheet current magnetic fields in one embodiment of a sheet currentflow model where magnetic field measurements are taken at threepositions above a ground surface;

FIG. 6 illustrates details of an example embodiment of a three sensorburied object locator magnetic field sensor line tracing operation;

FIG. 7 illustrates details of a process for determining the depth of aburied object in a locator using a sheet current flow model with sensorsrotated at a slight angle from a buried object vertical centerline;

FIG. 8 illustrates details of a process for determining the depth of aburied object in a locator using a sheet current flow model with sensorsat an offset translated position from a buried object centerline;

FIG. 9 illustrates details of an embodiment of a buried object locatorfor use in determining an estimated depth of a buried object byprocessing magnetic field measurements in accordance with a sheetcurrent flow model;

FIG. 10 illustrates details of an embodiment of a process fordetermining an estimated depth of a buried object based on three or moremagnetic field measurements at different positions using a sheet currentflow model;

FIG. 11 illustrates details of an embodiment of a process fordetermining an estimated depth of a buried object based on threemagnetic field measurements using a closed-form three measurement sheetcurrent flow model;

FIG. 12 illustrates details of a process for determining an estimateddepth of a buried object based on three magnetic field measurementstaken with a single magnetic field sensor and inertial position sensingusing a sheet current flow model;

FIG. 13 illustrates details of an alternate locator embodiment includinga distance sensor element to determine a distance between a locatorreference point and ground;

FIG. 14 illustrates details of an embodiment of a process fordetermining an estimated depth to a buried object using locators such asshown in FIG. 13 and FIG. 14;

FIG. 15 illustrates details of an embodiment of measurement andprocessing for determining an estimated depth of a buried object usingfour magnetic field sensor measurements; and

FIG. 16 illustrates details of an embodiment of a process fordetermining a buried object depth using measurements as shown in FIG.15.

DETAILED DESCRIPTION

In various embodiments, the teachings described herein may beimplemented in buried object locator devices and systems, such as inconjunction with those described in the following co-assigned patentsand patent applications: U.S. Pat. No. 7,336,078, entitled MULTI-SENSORMAPPING OMNIDIRECTIONAL SONDE AND LINE LOCATORS, issued Feb. 26, 2008;U.S. Pat. No. 7,332,901, entitled LOCATOR WITH APPARENT DEPTHINDICATION, issued Feb. 19, 2008; U.S. Pat. No. 7,276,910, entitledCOMPACT SELF-TUNED ELECTRICAL RESONATOR FOR BURIED OBJECT LOCATORAPPLICATIONS, issued Oct. 2, 2007; U.S. Pat. No. 7,136,765, entitledBURIED OBJECT LOCATING AND TRACING METHOD AND SYSTEM EMPLOYING PRINCIPALCOMPONENTS ANALYSIS FOR BLIND SIGNAL DETECTION, issued Nov. 14, 2006;U.S. Pat. No. 7,009,399, entitled OMNIDIRECTIONAL SONDE AND LINELOCATOR, issued Mar. 7, 2006; U.S. patent application Ser. No.11/054,776, entitled BURIED OBJECT LOCATING AND TRACING METHOD ANDSYSTEM EMPLOYING PRINCIPAL COMPONENTS ANALYSIS FOR BLIND SIGNALDETECTION, filed on Feb. 9, 2005; U.S. patent application Ser. No.61/614,829, entitled QUAD-GRADIENT COILS FOR USE IN LOCATING SYSTEMS,filed on Mar. 23, 2012; and U.S. patent application Ser. No. 11/774,462,entitled SYSTEM AND METHODS FOR LOCATING BURIED PIPES AND CABLES WITH AMAN PORTABLE LOCATOR AND A TRANSMITTER IN A MESH NETWORK, filed Jul. 6,2007, scheduled to be issued as U.S. Pat. No. 8,264,226 on Sep. 11,2012. The content of each of these applications is incorporated byreference herein in its entirety. These applications may be collectivelyreferred to herein as the “incorporated applications.”

The present disclosure relates generally to systems and methods forlocating buried or hidden objects. More particularly, but notexclusively, the disclosure relates to systems, methods, and apparatusfor locating buried objects using magnetic fields emitted from theobject and determining and displaying an estimate of the distance/depthof the object based on three or more magnetic field measurements takenat different positions relative to the buried object. The three or moremagnetic field measurements may be processed in accordance with a sheetcurrent flow model to determine the distance/depth estimate. Themagnetic field measurements may be taken by moving a single magneticfield sensor to multiple positions for taking measurements, and/or bytaking measurements from multiple magnetic field sensors offset a knownrelative distance from each other. The multiple sensors/antennas offseta known relative distance may be moved as a group to acquire magneticfield data at multiple points or along a multiplicity of paths throughspace above the ground.

For example, in one aspect, the disclosure relates to a method fordetermining the depth of a buried object by taking three or moremagnetic field measurements, either by using a single magnetic fieldantenna/sensor located at three positions relative to the buried object,or by taking measurements from two or more magnetic field sensors offsetat a known relative position to each other.

In an exemplary embodiment, a locator may include three magnetic fieldantennas co-linearly located at known relative distances from eachother. The three antennas may be vertically “stacked” relative to eachother during a locate operation to measure magnetic field components,including at least a horizontal magnetic field component at eachantenna, which may then be used to provide a closed-form estimate ofdistance/depth to the buried object. In addition, a locator may includetwo or more horizontally offset magnetic field antennas for locating acenterline or tangent line, from the ground, relative to the buriedobject, such as by equalizing magnetic field measurements in eachantenna/sensor to estimate the centerline. Outputs from the horizontaland vertical magnetic field sensors may be used to automaticallydetermine an optimal position above the buried object and the multiplemeasurements may be collected and processed, such as further describedbelow, to generate an estimate of the distance to the buried objectbelow the ground.

In another aspect, the disclosure relates to a method for locating aburied object with a buried object locator. The method may include, forexample, generating a first magnetic field measurement at a firstposition, generating a second magnetic field measurement at a secondposition different from the first position, generating a third magneticfield measurement at a third position, which may be different from thefirst and second positions, and processing the first, second, and thirdmagnetic field measurements in accordance with a sheet current flowmodel to generate an estimated distance/depth to the buried object.

The first, second, and third positions may, for example, be co-linear ona line. The line may be oriented along a vertical centerline extendingupward from the buried object and ground surface. The verticalcenterline may be a tangent line from the buried object and extendingupward from the ground surface. Alternately, the line may be offset atan angle from the vertical centerline. Alternately, or in addition, thefirst, second, and third positions may be co-linear on a line translatedhorizontally from the vertical centerline.

The measurements at the first, second, and third positions may, forexample, be generated by corresponding first, second, and third antennasensors. The measurements at the first, second, and third positions maybe generated simultaneously or may be generated at different times.Alternately, the measurements at the first, second, and third positionsmay be generated by one or two antenna sensors.

The sheet current flow model may include, for example, a magnetic fieldcomponent modeled as being generated by an infinite sheet current. Inaddition, the sheet current flow model may include an additionalmagnetic field component modeled as being generated by a current flowingin a buried conductor. Alternately, the sheet current flow model mayinclude an additional magnetic field component modeled as beinggenerated by a magnetic dipole antenna disposed within the buriedobject. Alternately, the sheet current flow model may include a magneticfield component modeled as being generated by a finite sheet current.The finite sheet current may be modeled as being non-uniform.

The first and second positions may, for example, be at a first distancerelative to each other, and the second and third positions may at asecond distance relative to each other, and the first distance may bedifferent than the second distance.

The sheet current flow model may include, for example, a model of asheet current flowing in a ground material in proximity to a groundsurface and a model of a conductor current flowing in a conductordisposed at a distance below the ground surface. The sheet current andthe conductor current may flow in substantially opposite directions. Thesheet current flow model may represent an infinite current sheet andcorresponding magnetic field. The sheet current flow model may representa finite current sheet and corresponding magnetic field. The sheetcurrent flow model may be represented by a closed-form equationsolution.

Alternately, the sheet current flow model may be represented by anopen-form equation solution, and the method may further include solvingthe open-form equation. The open-form equation may be iteratively solvedto determine the distance/depth estimate. The open-form equation may benumerically solved.

The method may further include, for example, automatically determiningan optimal measurement position above the ground to the buried object.The method may further include generating and processing the magneticfield measurements responsive to the automatically determining anoptimal measurement position. The automatic determination of an optimalmeasurement position above the ground may include determining a verticalcenterline through the buried object. The vertical centerline may bedetermined by using one or more horizontally oriented magnetic fieldsensors.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example, amagnetic field sensor assembly. The magnetic field sensor assembly mayinclude one or more magnetic field sensors configured to generate first,second, and third magnetic field measurement information atcorresponding first, second, and third positions, a memory module, and aprocessor module coupled to the memory. The processor module may beconfigured to receive the first, second, and third magnetic fieldmeasurement information, and process the received first, second, andthird magnetic field measurement information in accordance with a sheetcurrent flow model to generate an estimated distance to the buriedobject.

The magnetic field sensor assembly may include, for example, a firstmagnetic field sensor module configured to generate the first magneticfield measurement information, a second magnetic field sensor moduleconfigured to generate the second magnetic field measurementinformation, and a third magnetic field sensor module configured togenerate the third magnetic field measurement information. Alternately,or in addition, the magnetic field sensor assembly may include alocation determination module, and a magnetic field sensor moduleconfigured to generate the first magnetic field measurement information,the second magnetic field measurement information, and the thirdmagnetic field measurement information based at least in part oninformation provided from the location determination module.

In another aspect, the disclosure relates to a non-transitorymachine-readable medium containing processor-executable instructions.The processor-executable instructions may cause a processor element orcomputer to receive first, second, and third magnetic field measurementinformation, and process the received first, second, and third magneticfield measurement information in accordance with a sheet current flowmodel to generate an estimated distance to a buried object.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example,means for generating first magnetic field measurement information, meansfor generating second magnetic field measurement information, means forgenerating third magnetic field measurement information, means forreceiving the first, second, and third magnetic field measurementinformation, and means for processing the received first, second, andthird magnetic field measurement information in accordance with a sheetcurrent flow model to generate an estimated distance to the buriedobject.

In another aspect, the disclosure relates to a method for locating aburied object with a buried object locator. The method may include, forexample, generating, in the locator, a first magnetic field measurementat a first position, generating, in the locator, a second magnetic fieldmeasurement at a second position different from the first position,generating, in the locator, a third magnetic field measurement at athird position different from the first and second positions, andstoring the first, second, and third magnetic field measurements andassociated position information in a memory of the locator. The methodmay further include processing, in a processing element of the locatoror other electronic computing system, the first, second, and thirdmagnetic field measurements and associated position information. Themeasurements and position information may be processed in accordancewith a closed-form sheet current flow model to generate an estimate ofthe depth, Db, of the buried object below a ground surface. The methodmay further include storing the estimated depth in the memory. Themethod may further include providing a visual display of the estimateddepth on a display of the locator or other device. The method mayfurther include sending the estimated depth to an external electroniccomputing system via a wired or wireless connection.

The first, second, and third positions may be, for example,substantially co-linear on a line intersecting the buried object. Theline may be along a vertical centerline extending upward from the buriedobject and ground surface. The line may be offset at an angle ofapproximately ten degrees or less from a vertical centerline extendingupward from the buried object and ground surface. The first, second, andthird positions may alternately be co-linear on a line translatedhorizontally from a vertical centerline extending upward from the buriedobject and ground surface.

The measurements at the first, second, and third positions may, forexample, be generated by corresponding first, second, and third magneticfield antenna sensors. The measurements at the first, second, and thirdpositions may be generated substantially simultaneously by the first,second, and third magnetic field antenna sensors. Alternately, themeasurements at the first, second, and third positions may be generatedsequentially by a single magnetic field antenna sensor moved between thefirst, second, and third positions. Alternately, the measurements at thefirst, second, and third positions may be generated by two magneticfield antenna sensors moved between two or more of the positions.

The sheet current flow model may include, for example, a magnetic fieldcomponent modeled as being generated by an infinite sheet current andanother magnetic field component modeled as being generated by a currentflowing in a buried conductor. The estimate of the buried object depth,D_(b), may be determined using a closed-form sheet current flow model.The sheet current flow model may include a magnetic field componentmodeled as being generated by a finite sheet current. The first andsecond positions may be at a first distance relative to each other andthe second and third positions may be at a second distance relative toeach other. The first distance may be different than the second distanceor, in some embodiments, may be the same distance. The sheet currentflow model may include a model of a sheet current flowing in a groundmaterial in proximity to a ground surface and a model of a conductorcurrent flowing in a conductor disposed at a distance below the groundsurface.

The sheet current flow model may, for example, be represented by anopen-form equation solution rather than a closed-form solution. Themethod may further include solving the open-form equation. The open-formequation may be iteratively solved in the locator or other electroniccomputing system.

The method may further include, for example, automatically determiningan optimal measurement position above the ground to the buried object,and generating and processing the magnetic field measurements responsiveto the automatically determining an optimal measurement position. Theautomatically determining an optimal measurement position above theground may include determining a centerline using one or morehorizontally oriented magnetic field sensors to provide information toposition the locator over the buried object.

The method may further include, for example, storing a specification ofa buried object depth in the locator, comparing the estimated depth tothe specification depth, and providing, responsive to the comparison, anotification. The notification may include providing an operator alarm,display, audio, or visual indication if the estimated depth is less thanthe specification and/or storing information associated with theestimated depth, specification, and/or out of specification distance ofthe estimated depth. The notification may include storing a databaseentry indicative of the difference between the estimated depth and thespecification.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example, amagnetic field sensor assembly. The magnetic field sensor assembly mayinclude one or more magnetic field sensors configured to generate first,second, and third magnetic field measurement information atcorresponding first, second, and third positions, one or more memorymodules, and one or more processing modules coupled to the memory. Theprocessing modules may include one or more processing elementsconfigured to receive the first, second, and third magnetic fieldmeasurement information, process the received first, second, and thirdmagnetic field measurement information in accordance with a closed-formsheet current flow model to generate an estimated distance to the buriedobject, store the estimated depth in the memory, and provide a visualdisplay of the estimated depth on the locator.

The magnetic field sensor assembly may include, for example, a firstmagnetic field sensor module configured to generate the first magneticfield measurement information, a second magnetic field sensor moduleconfigured to generate the second magnetic field measurementinformation, and a third magnetic field sensor module configured togenerate the third magnetic field measurement information. The magneticfield sensor assembly may include a location determination module, and amagnetic field sensor module configured to generate the first magneticfield measurement information, the second magnetic field measurementinformation, and the third magnetic field measurement information basedat least in part on information provided from the location determinationmodule. The estimated depth, D_(b), may be determined in the processormodule using a closed-form sheet current flow model.

In another aspect, the disclosure relates to a non-transitorymachine-readable medium containing processor-executable instructions forcausing a computer to receive first, second, and third magnetic fieldmeasurement information, and process the received first, second, andthird magnetic field measurement information in accordance with a sheetcurrent flow model to generate an estimated depth of a buried objectbelow a ground surface.

In another aspect, the disclosure relates to a method for locating aburied object with a buried object locator. The method may include, forexample, generating, in the locator, a lower magnetic field measurementat a first locator position, generating, in the locator, an uppermagnetic field measurement at the first locator position, generating, inthe locator, a lower magnetic field measurement at a second locatorposition different from the first position, generating, in the locator,an upper magnetic field measurement at the second locator position,storing the first and second locator position lower and upper magneticfield measurements in a memory of the locator, processing the first andsecond position lower and upper magnetic field measurements inaccordance with a closed-form sheet current flow model to generate anestimate of the depth, D_(b), of the buried object below a groundsurface, and storing the estimated depth in the memory. The estimate ofthe buried object depth, D_(b), may be determined using a closed-formsheet current flow model.

In another aspect, the disclosure relates to a locator for determiningthe location of a buried object. The locator may include, for example, amagnetic field sensor assembly. The magnetic field sensor assembly mayinclude a plurality of magnetic field sensors configured to generatelower and upper magnetic field measurement information at first and asecond locator positions, a memory module, and a processor modulecoupled to the memory, wherein the processor is configured to processthe first and second position lower and upper magnetic fieldmeasurements in accordance with a closed-form sheet current flow modelto generate an estimate of the depth, D_(b), of the buried object belowa ground surface, store the estimated depth in the memory, and provide avisual display of the estimated depth on the locator. The estimateddepth, D_(b), may be determined in the processor module using aclosed-form sheet current flow model.

The following exemplary embodiments are provided for the purpose ofillustrating examples of various aspects, details, and functions ofapparatus and systems; however, the described embodiments are notintended to be in any way limiting. It will be apparent to one ofordinary skill in the art that various aspects may be implemented inother embodiments within the spirit and scope of the present disclosure.

It is noted that as used herein, the term, “exemplary” means “serving asan example, instance, or illustration.” Any aspect, detail, function,implementation, and/or embodiment described herein as “exemplary” is notnecessarily to be construed as preferred or advantageous over otheraspects and/or embodiments.

Before describing various aspects further, an overview of the buriedobject locator (“tracing”) problem, along with various constraints andvariables, is described below.

Turning to FIG. 1, an example locator 100, which may include a magneticsensor assembly 110 and a control unit 120, is shown positionedvertically above the ground 180. The magnetic sensor assembly 110 mayinclude one or more magnetic field antennas/sensors, such as antennas111, 112, and 113 as shown, which may be single axis or multi-axis(e.g., three axis) magnetic field sensors. Two or three axis magneticsensors may be omnidirectional nested sensor arrays for measuringorthogonal magnetic field components in two or three directions.

Control unit 120 may include elements such as a user interface, one ormore displays or other visual or audio outputs, one or more controlinputs, as well as electronics for processing signals received from thesensors of the sensor assembly and memory for storing generatedinformation.

The electronics may include analog or digital electronic circuits forsignal condition, analog-to-digital conversion, as well as processorelements and associated memory for storing data and instructions forprocessing the received sensor signals. Other elements, such as inertialnavigation elements, GPS or other position sensing elements, additionalmagnetic field sensors (e.g., horizontally oriented magnetic fieldsensors for determining a centerline of the buried object),accelerometers, compass sensors, magnetometers, as well as otherelements, such as wired or wireless transmitters and receivers, may beincorporated in or use in conjunction with a locator such as locator100.

In operation, locator 100 is typically moved about above the groundsurface (180 deg.) to attempt to locate a buried object 150, such asconduit or other buried pipe (shown in cross-section in FIG. 1), whichruns into and out of the plane (i.e.—out of the page) as shown inFIG. 1. The buried object or an element associated with a buried object(e.g., a wire, which may be commonly referred to as a “tracer wire”,added to or placed adjacent to a non-conducting pipe) carries current,which may be inherent in the buried object (e.g., as in a buried powertransmission line) or may be coupled to or induced into the buriedobject by a transmitter or other device.

The buried object 150 is located at a distance or depth D_(b) relativeto the surface of the ground 180, while the lower sensor element ispositioned at a distance H above the ground surface. Since the buriedobject is sensed relative to the sensor location, an additionalcorrection may be made to adjust the estimated depth to account for theoffset of the sensors 111, 112, and 113 above the surface of the ground.For example, while the results from processing information from sensors111, 112, and 113 (or other combinations of sensors and/or positions)may provide an estimate of the distance from the buried object to theposition of the lower sensor 111 (i.e., D1 as shown in FIG. 1), thedepth below the ground may be determined by subtracting a known ormeasured height, H, from a measurement referenced to the buried objectby distance D1.

An operator moves the locator over the ground to determine positioningof the buried object (e.g. along the surface of the ground, in the X-Yplane or ground plane) as well as the depth of the buried object (Z orup/down axis). Depth may change as the buried object may have beenplaced in a trench or other excavated volume, and/or the terrain maychange, thereby changing the depth of the buried object relative to theground surface as the operator's position over the ground changes.Before digging or performing other operations that could affect theburied object, it may be very desirable to determine an estimated depthto the buried object at one or more positions, along with a surface mapof the positions or path of the object along the surface as well asdepth of the object below the surface.

One characteristic of the ground in many areas is that it is nothomogenous. This may be due to various reasons, such as compaction, suchas by a sheeps foot tool, deposition, layering of different substratematerials over time and/or shifts or uplifts in the ground over time,excavation and backfill, amount of water provided to the ground andwater penetration, construction near the ground surface, as well as forother reasons. These may result in anisotropic soil conditions—forexample, trench backfill is usually inhomogeneous and anisotropic.

FIG. 2 illustrates a diagram 200 showing an example ground cutaway viewwith various elements that may affect ground homogeneity as well asassociated ground conductivity, which affects current flow within theground when measurements are being made with sensing assembly 110 oflocator 100. For example, the ground may include a grass or turf surface260, which may vary across the ground surface, and which may havevarious materials below it, such as compost, peat moss, fertilizers,etc., which may affect conductivity. Below the surface, the type ofmaterial, as well as the strike and slope (e.g., direction and angle) ofmaterial layering, may vary. For example, a first type of soil 230 or250 may be near the ground surface, while a different type of soil 240may be further below. Soils 230, 240, and 250 may include differentminerals, etc. (e.g., sand, clay, rock, etc.), that may affect theirconductivity.

Other differences in the ground structure may include a trench, such astrench 210 as shown, which may have been excavated to place buriedobject 150, and may be backfilled with a different material 220 than thesurrounding soil (e.g., soils 230, 240, 250). In this case, the trenchand backfill in proximity to the buried object may have small to largedifferences in conductivity than the adjacent soils.

Other features may also affect conductivity. For example, constructionfeatures, such as concrete sidewalk or slab 270, may be placed in theground, further affecting the ground characteristics. In various locatoroperations, ground areas having one or more of these inhomogeneouscharacteristics (or others not specifically illustrated) may be present.Differences in ground characteristics may affect locator operation, suchas by affecting return current flow (typically through the ground),distorting magnetic fields above the ground, or otherwise affecting thesignals received by the locator's sensors.

FIG. 3 illustrates details of an example locator sensor (line tracing)operation above a buried object such as object 150. As shown in FIG. 3,the buried object may have a current coupled to it from a transmitter310 as shown (e.g., via cabling and clamps/connectors 362 and 370) to anaboveground stub or other contact 364. In some cases, such as withburied transmission lines, current flow is inherent in the buriedobject, and therefore no signal need by coupled to the object as shownin FIG. 3. In some cases, currents may be induced onto the buriedobject, such as by low frequency commercial or military radio signals orother electromagnetic field sources.

Current 320 flows through the buried object such as shown and eventuallyreturns through the ground as ground return currents 322. If atransmitter is used, the ground return current 322 may flow to a stakeor other object 330 in the ground, where it may then be coupled back tothe transmitter via a cable 332. Return currents from buried power lineswill similarly return to a source through the ground.

Magnetic fields 325, generated by current 320 flowing through the buriedobject conductor 150, may be measured by a magnetic field antenna/sensor340, which may correspond with sensors 111, 112, and/or 113 of FIG. 1.The sensor outputs may be provided via a cable or printed circuit boardconnection 346 to additional processing electronics, which may belocated in control unit 120. The magnetic fields will typically besensed in multiple directions, such as in three orthogonal directionscorresponding to the X and Y plane (the X and Y plane is approximately alocal tangent to the geoid as shown in FIG. 3, as well as the Z axis(vertical in FIG. 3).

Based on the path of the return current 322 through the ground, anadditional magnetic field component (now shown in FIG. 3), which mayhave a directional component opposite that of the outbound current 320,may be generated by the ground flow current. The ground flow currentpath will be dependent on a number of factors, including the groundcharacteristics (such as those described with respect to FIG. 2), aswell as frequency, etc. In one aspect, embodiments of the presentdisclosure may be used to estimate these ground characteristics bytaking multiple sensor measurements while moving around the vicinity ofthe buried object and matching the sensed values with position dataobtained by inertial systems, GPS receivers, etc. In addition, a sheetcurrent flow model may be used to generate an enhanced buried objectdepth measurement by adjusting for the ground return current, such asdescribed subsequently.

Turning to FIG. 4, a diagram 400 showing details of an embodiment of asheet current flow model that may be used to approximate the groundreturn current flow in the proximity of the buried object conductor 150is shown. In general, a sheet current flow model includes a sheetcurrent flow component and associated sheet current magnetic field,which is associated with ground return current flow, as well as aconductor current flow component and associated conductor currentmagnetic field, which is associated with current flow in the buriedobject, or, in the case of use of a sonde, magnetic fields associatedwith a dipole antenna disposed within or in proximity to the buriedobject.

For example, an outward current flow 420 (which may correspond tocurrent 320 of FIG. 3) may be returned via ground return current 422(which may correspond with current 322 of FIG. 3). Depending on thecharacteristics of the ground, a portion of the ground return current424, which may be modeled as a sheet current, may be present at or nearthe ground surface as shown and may concomitantly generate acorresponding magnetic field. In some cases, the sheet current may bemodeled as an infinite current sheet, depending on the groundcharacteristics and frequency. In other cases, the sheet current may bemodeled as a finite current sheet, which may have tapered current valuesmoving away from the centerline 450 of the buried object, or mayotherwise be adjusted based on particular ground characteristics, whichmay be asymmetric about the centerline. Outward conductor current flow420, which may be coupled to or induced in the buried object 150, or maybe inherent (in the case of buried power transmission cables), generatesa magnetic field component surrounding the buried object, which maylikewise be sensed by the locator.

FIG. 5 illustrates a diagram of an embodiment 500 of a measurementconfiguration for determining an estimate of the depth of a buriedobject 150. In this configuration sensor measurements may be taken atthree positions for use with a three magnetic field measurement sheetcurrent flow model for determining an estimated depth of buried object150. The three magnetic field measurement solution as shown in equation(1) may be used for this configuration. As shown in FIG. 5, three sensorpositions, denoted as P₁, P₂, and P₃, approximately along verticalcenterline 450 (approximately perpendicular to the ground surface orlocal geoid), where magnetic field measurements may be taken, are shown.The three positions may correspond with a single sensor moved betweenthe three positions to take separate measurements, or for two or moresensors to take measurements at the three positions. In an exemplaryembodiment, three magnetic field sensors may be used to simultaneouslytake measurements at the three points, such as in a three sensorlocator, such as locator 100 as shown in FIG. 1; however, other numbersof sensors may also be used to take the three measurements in variousembodiments, such as single sensor or two sensor locators. Thecenterline may be known, approximated, or measured, such as by usingadditional magnetic sensors in a horizontal orientation (not shown) toposition the locator directly over the buried object. Example of thistype of sensor configuration and operation in described in theincorporated applications and in particular in U.S. patent applicationSer. No. 61/614,829, the content of which is incorporated herein byreference.

At each sensor position (e.g., P₁, P₂, and P₃), one magnetic fieldcomponent B_(cc) (representing the B-field generated by the conductorcurrent (cc)) may be present that is generated by the buried objectconductor 150. In some embodiments, the magnetic field component may beat multiple frequencies, which may be selected to provide enhancedresolution, distance/depth estimation performance, signal processingperformance, or other functions. For example, in some embodiments, atransmitter, such as transmitter 310 as shown in FIG. 3, may beconfigured to provide current at multiple frequencies, such as two ormore of the frequencies described previously with respect to FIG. 3.Example field lines 510 for the conductor current magnetic field areshown.

In addition, a second magnetic field component, B_(sc) (representing theB-field generated by the sheet current (sc) component 424 of the groundcurrent 322), generated by the sheet current, may also be present ateach sensor position. In general, at each sensor position, a componentof both the conductor current and sheet current will be superimposed togenerate the resulting measured magnetic field at each point. Examplesof these fields are shown as field lines 520, which, in accordance withone sheet current flow model, are substantially constant and independentof distance from the ground (i.e., approximate a constant field as wouldbe generated by an infinite current sheet).

In general, it may be desirable to separate the first and second sensorsand the second and third sensors by different distances in the verticaldirection (and/or, in some embodiments, horizontal offsets (not shown))of the sensor positions relative to the orientation shown in FIG. 5. Thevertical separations or distances are shown in the example of FIG. 5 asS₁₋₂ and S₂₋₃, respectively. As described subsequently herein, thesedistances may be used in a closed-form solution model, where theclosed-form model variable sep₁ corresponds with S₁₋₂, and theclosed-form model variable sep₂ corresponds with S₁₋₂+S₂₋₃. In FIG. 5,the distance from the lower measurement position P₁, is typically afinite distance, H, vertically above the ground surface, and thevertical distance from the buried object 150 to position P₁ is adistance D₁. The depth of the buried object below the ground, D_(b), maybe determined by subtracting H from D₁. As described subsequentlyherein, the height, H, may be determined based on a known referenceheight above the ground, through use of a distance sensor oraccelerometer-based distance measurement device, or by other distancemeasurement methods known or developed in the art. If a sensor is used,the distance information may be provided to a processing element of thelocator, along with the magnetic field measurements, to solve for theestimated depth as describes subsequently herein using sheet currentflow model solutions.

In general, the magnetic field components B_(cc) and B_(sc) will varydifferently as a function of the distance, D_(n), between the buriedobject conductor 150 and sensor positions, P_(n). Consequently, at eachsensor position, the sensor reading may be represented asB_(cc)(D_(n))+B_(sc) (D_(n)) (e.g., the total magnetic field reading ateach position is a sum of a first function representing B_(cc) as afunction of D_(n) and a second function representing B_(sc) as afunction of D_(n)).

For example, for current flowing in a line conductor, the magnetic fielddrops off approximately proportionally to 1/D_(n) (the field may beaffected, however, by various factors, including the frequency, groundconductivity and conductivity variation, etc.). Using this estimate, theB_(cc) field at each sensor position is as follows (whereB_(cc)(D_(n))[P_(n)] is the B_(cc) value at position P_(n)):B _(cc) [P ₁ ]=k/D ₁B _(cc) [P ₂ ]=k/D ₂(where D ₂ =D ₁ +S ₁₋₂)and:B _(cc) [P ₃ ]=k/D ₃(where D ₃ =D ₂ +S ₂₋₃)

As noted previously, in some cases, the ground return sheet current mayapproximate an infinite sheet current. As is known, the magnetic fieldabove an infinite sheet current is a constant. Consequently, in oneembodiment, the B_(sc) value is independent of D_(n), and is the sameconstant value (denoted as B_(const) at each sensor position). Usingthis sheet current flow model, the measured magnetic field value (B₁,B₂, and B₃) at each sensor position can be written as follows:B ₁ =k/D ₁ +B _(const)B ₂ =k/D ₂ +B _(const)B ₃ =k/D ₃ +B _(const)

If sensor measurements (i.e., B₁, B₂, B₃) are taken at each position(P₁, P₂, and P₃), and the relative offsets between sensors 1, 2, and 3(S₁₋₂ and S₂₋₃) and k are known or determined, the equations can besolved for D₁, which can then be converted to a depth measurement to theburied object 150.

One possible closed-form sheet current flow model solution to theabove-described equation model that may be used to solve for a buriedobject depth estimate is described below: In this model, a closed formsheet current flow depth estimate solution may be implemented using (1)below:

$\begin{matrix}{D_{b} = {\frac{( {{- B_{m}} + B_{t}} )*{sep}_{1}*{sep}_{2}}{{- ( {B_{t}*{sep}_{1}} )} + {B_{b}*( {{sep}_{1} - {sep}_{2}} )} + {B_{m}*{sep}_{2}}} - H}} & (1)\end{matrix}$The variable for this closed-form sheet current flow model are (thesevariables are as shown in FIG. 5):

-   -   D_(b) is the estimated depth of the buried object below the        ground surface;    -   D₁ is the distance between the buried object and bottom sensor        position (P₁);    -   B_(b) is the measured magnetic field component at the bottom        sensor position (P₁);    -   B_(m) is the measured magnetic field component at the middle        sensor position (P₂);    -   B_(t) is the measured magnetic field component at the top sensor        position (P₃);    -   sep₁ is the distance, S₁₋₂, between P₁ and P₂;    -   sep₂ is the distance, S₁₋₂+S₂₋₃; between P₁ and P₃; and    -   H is the height or distance of the lower sensor position, P₁,        above the ground surface.

The three measurement position sheet current flow model solutiondescribed above was generated with the Mathematica software application.In an exemplary embodiment a three sensor locator may be used, however,a single sensor or two sensor locator may also be used with similarmeasurement and processing applied to measured magnetic field data. Itis noted that the distance-related variables such as sep, sep₁ and sep₂,H, etc., need to be in the same units or converted during processing toconsistent units. Likewise, current and magnetic field units need to becollected in or converted to consistent units, and parameters such asfree space permeability and the sensitivities of the various sensorsshould be accounted for in processing.

Another possible closed-form solution to the above-described equationsthat may be used is described below. In this model, it is assumed thatfour magnetic field sensor measurements are taken. In an exemplaryembodiment, this may be done using a two sensor locator and taking apair of measurements at different heights, as shown in FIG. 15 anddescribed in process embodiment 1600 of FIG. 16. Alternately, a singlesensor may take four separate measurements or other permutations ofsensor arrays and measurements may be done (e.g., a three sensor locatortaking two measurements to get at least four measurements at differentpositions, or a single sensor locator taking four measurements atdifferent positions, etc.).

FIG. 15 illustrates additional details of an exemplary embodiment wherea two sensor locator with a two sensor array 1510 is used. In thisconfiguration, the locator array 1510 includes two ball-shapedomnidirectional magnetic field sensors 1511 and 1512, which areseparated by a known distance or separation, sep. A buried conductor 150is at a depth D_(b) below the surface of the ground 180 as shown. At afirst measurement stage, a first set of magnetic field measurements maybe taken at a first height, H₁, above the ground with measurements takenat positions P_(1b) and P_(1T), corresponding to the positions of thebottom 1511 and top 1512 sensors. If the lower sensor is rested on theground, the first height, H₁, may be a known value as a function of thelocator geometry. For example, if the lower sensor is a ball assembly atthe bottom of the locator (as shown), H₁ will be the ball radius,r_(ball). In other embodiments, H₁ may be measured directly such asdescribed herein using a distance measuring element such as an acousticor optical distance measurement sensor, an accelerometer, or anelectromechanical or other distance measurement element.

At measurement stage 2, the locator may be moved upward (vertically) asshown to height H₂ above the ground, and a second set of magnetic fieldmeasurements may be taken at positions P_(2b) and P_(2T).

These measurements may then be processed in a closed-form sheet currentflow model of the form:

$\begin{matrix}{\mspace{79mu}{D_{b} = {\frac{L + M}{N} - H_{1}}}} & (2) \\{\mspace{79mu}{{Where}\text{:}}} & \; \\{\mspace{76mu}{L = {( {B_{1\; b} - B_{1\; T}} )*( {B_{1\; T} - B_{2\; T}} )*( {B_{1\; b} + B_{1\; T} - B_{2\; b} - B_{2\; T}} )*{sep}}}} & (3) \\{M = \sqrt{\begin{matrix}{( {B_{1\; b} - B_{1\; T}} )*( {B_{1\; b} - B_{2\; b}} )*( {B_{1\; T} - B_{2\; T}} )*( {B_{1\; b} + B_{1\; T} - B_{2\; b} - B_{2\; T}} )^{2}*} \\ {( {B_{2\; b} - B_{2\; T}} )*{sep}^{2}} )\end{matrix}}} & (4) \\{N = {( {B_{1\; b} - B_{1\; T}} )*( {B_{1\; b} + B_{1\; T} - B_{2\; b} - B_{2\; T}} )*( {B_{1\; b} - B_{1\; T} - B_{2\; b} + B_{2\; T}} )}} & (5)\end{matrix}$And where the variables for this model are:

-   -   B_(1b) is a first magnetic field measurement taken at the lower        or bottom ball of the two balls;    -   B_(1T) is a first magnetic field measurement taken at the upper        or top ball of the two balls;    -   B_(2b) is a second magnetic field measurement taken at the lower        or bottom ball of the two balls;    -   B_(2T) is a second magnetic field measurement taken at the upper        or top ball of the two balls;    -   sep is the distance between the lower and upper sensors/antenna        balls;    -   H₁ is the distance of the lower sensor above the ground at the        first measurement position.

FIG. 16 illustrates a corresponding embodiment of a process 1600 forperforming a buried object depth estimate corresponding to the exampleshown in FIG. 15. Process 1600 may begin at stage 1610, where a firstset of magnetic field measurements (at two points relative to a firstmeasurement position) are taken. The two points may be separated by aknown distance, sep, which may be the fixed distance between twomagnetic field sensors on a locator sensor assembly, such as assembly1510 of FIG. 15.

At stage 1620, the locator may be moved upward (or in some uses,downward) to a second measurement position. A second set of magneticfield measurements at two points may be then be taken. At stage 1630,the measurement taken at the first and second locator positions may thenbe processed using a sheet current flow model solution such as describedpreviously herein in equations (2)-(5).

The two sensor, two measurement position sheet current flow modelsolution described above was similarly generated with the Mathematicasoftware application. A two sensor locator is assumed, with verticalnavigation used to get magnetic field measurements at four positions asshown in FIG. 15. It is noted that, in other configurations, locatorshaving three or more antenna/sensors could be used to take simultaneousmeasurements, single antenna/sensor locators could be used to take fouror more measurements, or other permutations could may also be used.

At locator position 1 (i.e., a two sensor locator taking measurements attop and bottom positions), measurements B_(1b) and B_(1T) are taken. Thelocator is then moved to a second position, where two additionalmeasurements, B_(2b) and B_(2T) are taken. Based on these fourmeasurements and using the sheet current flow model (which in thisexample assumes an infinite sheet current with a constant magnetic fieldcomponent and a conductor current having a 1/D magnetic field componentin the horizontal direction) the resulting distance/depth determinationas shown in FIG. 15 can also be determined as:

$\begin{matrix}{D_{1} = \frac{( {B_{1\; T} - J_{sheet}} )*{sep}}{B_{1\; b} - B_{1\; T}}} & (6) \\{D_{2} = \frac{( {B_{2\; T} - J_{sheet}} )*{sep}}{B_{2\; b} - B_{2\; T}}} & (7)\end{matrix}$and the sheet current, J_(sheet), is given by:

$\begin{matrix}{J_{sheet} = \frac{\begin{matrix}{{( {B_{1\; T} + B_{2\; b} - B_{2\; T}} )*J} -} \\{{B_{2\; b}*B_{2\; T}*{sep}} + {B_{1\; b}( {{- J} + {B_{1\; T}*{sep}}} )}}\end{matrix}}{( {B_{1\; b} + B_{1\; T} - B_{2\; b} - B_{2\; T}} )*{sep}}} & (8)\end{matrix}$where J is the current flowing in the buried object/wire and sep is theseparation between the top and bottom sensors. This solution assumesthat J and sep are non-zero.

In the case where the lower sensor is a ball or sphere-typeomnidirectional magnetic field sensor and the ball is position on theground, D_(b) is approximately D₁, differing only by the distance fromthe sensor's sensing position (e.g., the center of a sphere when aball-type sensor is used) to the ground, or the ball's radius, r_(ball).In this case, with the ball radius know, D_(b) can be solved as:D _(b) =D ₁ −H ₁ =D ₂ −H ₂ =D ₁ −r _(ball)  (9)

In some embodiments, depth estimates may be determined by using two ormore processing methods and cross-checking the results. For instance, inthe above example, which uses a buried object and actual collected data,where actual depth was 1600 millimeters, the D₁ depth estimate is 1618mm, and the D₂ depth estimate is 1719 millimeters. These results were animprovement over the traditional depth estimate results of 1378 mm, and1451, respectively, using traditional processing algorithms.

Collection of magnetic field measurement data for processing ofmeasurement data as described above for the three or four measurementpoint solutions described above may be done in various ways. Forexample, a single locator with three sensors may be used to collectthree measurements and, if the locator is positioned so the lower sensoris at a known distance above the ground (e.g., H), such as by being incontact with the ground, then the three magnetic field measurements maybe processed in accordance with sheet current flow model equation (1) todetermine the estimated depth to the buried object. Alternately, if athree sensor locator is used and the locator is positioned at somedistance above the ground, the distance to the ground may be measuredvia any of a variety of distance measuring devices such as a mechanicaldevice (e.g., rod, measuring stick, etc), optical device (e.g., laser,infra-red), acoustic measurement device, inertial/accelerometer-based,or other distance measurement device known or developed in the art.Combining the distance measurement from the locator to the ground withthe three magnetic field measurements similarly allows solution of theburied depth estimate using equation (1). A single sensor locator couldsimilarly be used to collect three (or more) measurements and associateddistance information and may be similarly processed using equation (1)or another closed or open-form sheet current flow model solution.

If a two sensor locator is used, pairs of measurements may be collectedat two locator positions, as shown in FIG. 15. These measurements maythen be processed using the sheet current flow model solution ofequations (2)-(5). If the first measurement set is taken with the lowersensor ball on or at a known position relative to the ground, noadditional distance measurement need to be taken in order to solve forthe buried object depth estimate. If more than two sensors or more thantwo locations are used, these additional measurements can be used tocalculate a mean estimate of the burial depth and characterize thequality of the measurement by calculating the variance as well as higherorder cumulants. These statistical properties can be compared against anexternal specification for generation of a quality metric of themeasurement which may be stored and/or displayed to a user on thelocator.

Alternately, a three sensor locator, such as shown in FIG. 1, could beused to do similar processing to that done by the two sensor locator ofFIG. 15, with just two of the three measurements taken at each positionused. This can similarly be done without specific distance measurementelements if the lower sensor is placed on or at a known positionrelative to the ground, or, alternately, with use of a distancemeasurement sensor to provide distance information associated with themagnetic field measurements. In the two sensor locator example, it isnoted that the four measurements should be at different positions andthat it is theoretically possible for a locator to be raised such thatthe lower sensor ball at the second measurement position is at the samepoint as the upper sensor ball was at the previous measurement. In atypical two-axis locator, the sensor balls are sufficiently far apartthat it would normally be difficult to raise the locator to such anamount that the lower and upper balls would overlap in position, andtherefore this condition would be unlikely to occur. However, it may beuseful to configure the locator and sensor measurements such thatmeasurements taken in such a configuration are non-possible or anoperator warning or rejection of the measurement is indicated if it doesoccur.

In addition, combinations or repeated measurements using theabove-described solutions may be used to provide multiple depthestimates that can be averaged or otherwise aggregated. For example, athree sensor locator may perform two sheet current flow model solutions,with one based on a three measurement solution and one based on a fourmeasurement solution.

FIG. 6 illustrates details of an example measurement operation using athree sensor locator to determine an estimate of the depth, D_(b), of aburied object 150 below the ground 180 surface. The lower part of alocator 600, which may correspond with locator 100 of FIG. 1, includes amast and a three magnetic sensor assembly 610 including ball-typeomnidirectional magnetic field sensors 611, 612, and 613 which may benon-uniformly spaced on the mast as shown by dimensions S₁₋₂ and S₂₋₃.Calculations using a sheet current flow model may be used as describedherein to solve for the distance D₁, to the lower sensor, such asthrough use of the sheet current flow model solution of equation (1) asdescribed previously herein. The height of a reference point on thesensor assembly above the ground is denoted by H, and, if the locator ispositioned in contact with the ground, H will be equal to the radius ofthe ball or sphere of the lower sensor 611 when the magnetic fieldmeasurement point is at the center of the sphere. The depth, D_(b), canbe estimated by subtracting H from D₁ as described previously.

FIG. 7 illustrates a diagram of an embodiment 700 of an alternatemeasurement configuration for determining an estimate of the depth of aburied object 150. In this configuration an estimated distance/depth ofa buried object below ground is based measurements at virtual positions(e.g., when the locator is offset from the vertical centerline and/orrotated relative to vertical). In the example configuration of FIG. 7,it is assumed that a locator is positioned offset from a centerline 450of the buried object (e.g., to the left or right when viewing the buriedobject in cross-section as shown). Three measurement positions, denotedas translated positions 1, 2, and 3 (TP_(n)) correspond with thelocation of sensor elements of the locator when translated from aposition over centerline 450. In addition, 2 virtual positions (VP_(n))may be defined corresponding to a radial 750 outward from the buriedobject conductor 150. Solving for the a distance estimate along radial750 may be done similarly to that described previously with respect toFIG. 5 using a sheet current flow model, with an additional step ofdetermining an angle of rotation of the translated positions, denoted asθ_(TR), and determining an estimate of the magnetic field componentsassociated with the sheet current flow model (e.g. the magnetic fieldmodel for the buried object conductor current and sheet current) at thevirtual positions). In an exemplary embodiment, if the sheet current isestimated as infinite as describe previously, the sheet current magneticfield component will be a constant, thereby requiring only an additionalestimate of the magnetic field of the buried object conductor 150 at thevirtual positions VP₂, VP₃ along with TP₁.

FIG. 8 illustrates a diagram of an embodiment 800 of an alternatemeasurement configuration for determining an estimate of the depth of aburied object 150. In this configuration an estimated distance/depth ofa buried object below the ground surface is based on sensor measurementsmade at an offset rotation/angle. In the example of FIG. 8, it isassumed that a locator is rotated at an angle θ_(R) from a centerline450 of the buried object (e.g. rotated to the left or right, at an anglefrom the centerline relative to an axis passing through the buriedobject conductor 150). In this example, three measurement positions,denoted as rotated positions 1, 2, and 3 (RP_(n)) correspond with thelocation of sensor elements of the locator when rotated from thecenterline 450 along radial 850. By determining the angle θ_(R) andtaking sensor measurements at the three rotated positions (RP₁, RP₂, andRP₃), the measurements can be processed similarly to the processingdescribed with respect to FIG. 5 using a sheet current flow model todetermine a distance/depth estimate. Since the magnetic field vectorwill become increasing distorted relative to the field taken in avertical orientation, analytical results suggest that the accuracy ofthe solution in the configuration of FIG. 8 will decrease as the angleθ_(R) increases. Consequently, it may be desirable to limit the rotationangle to ten degrees or less in order to obtain reasonably accurateresults using this approach.

In some embodiments, processing such as described with respect to FIGS.5, 7, and 8 may be combined, depending on the type of locator and/orlocator orientation, to determine the depth estimate. For example, alocator may be both offset and rotated relative to a centerline, inwhich case, a combination of translation and rotational processing, suchas described with respect to FIGS. 7 and 8, may be used.

FIG. 9 illustrated details of an embodiment of a locator 900 on whichvarious aspects as described herein may be implemented. Locator 900 mayinclude, for example, a locator receiver module 950, which may includeone or more magnetic field antennas/sensors, such as sensors 111, 112,and 113 of FIG. 1, or other magnetic field sensors described herein,along with additional electronics, such as signal conditioning circuits(not shown), signal processing module(s) 954, to further process thesignals, such as to filter the signals, digitize them, or perform othersignal processing functions, as well as additional components, such ashousings, etc. (not shown). In an exemplary embodiment, sensors 952 aremulti-axis sensors configured to perform simultaneous magnetic fieldsensing in two or more axes (typically three).

A user interface module 930 may be included to allow users to enterlocator parameters, such as frequency selections, sensor configurationinformation, display information, and/or other data or information. Anoutput/display module 970 may be included to provide output to a user,such as graphical information related to a locate operation, mappingdetails or information, audible information such as tones, synthesizedvoice output, and/or other data or information. Output module 970 may bepart of or integrated with user interface module 930 in someembodiments.

Locator 900 may include a processor module or element 940, which mayinclude one or more processing devices such as microprocessors,microcontrollers, digital signal processors, FPGAs, ASICs, and/or otherprogrammable devices. In addition processor module 940 may includeperipheral components, such as analog-to-digital converters, I/O(input/output) devices, communication modules, such as wireless, USB,Ethernet modules, etc., data storage modules, peripherals for providingdata output, such as USB ports for use with USB memory devices, and thelike. Processor module 940 may include and/or be coupled with one ormore memory module 945, which may be configured to store instructionsfor execution on the processor to perform functions as described herein,as well as to store locate data, data being processed in the device,and/or other data or information, such as location information,additional sensor information, environmental information, or otherinformation. An optional position module 910 may be included to provideposition information 915 to the processor module 940 and/or memorymodule 945. The positional information may be generated by positionsensing module 912 devices such as inertial navigation devices(accelerometers, gyroscopic devices, etc.), compass devices, and/orother position sensing devices, such as GPS modules or otherradionavigation modules. In operation, locator 900 may be configured toallow processor module 940 to receive sensor information from multiplesensor positions, such as those described previously with respect toFIGS. 6, 7, and 8, and determine information related to the buriedobject conductor (or a sonde, not shown), including a depth estimatebelow the ground.

FIG. 10 illustrates details of an embodiment of a process 1000 fordetermining an estimated depth to a buried object conductor. Process1000 may be used in locator device configurations, such as shown FIGS.1, 5, 6, 7, and 8, and may be implemented in a processor and memoryelement, along with coupled sensors, such as shown in FIG. 9.

At stage 1010, one or more sensor may receive magnetic field signalsfrom a buried object (or sonde) at three or more positions. In someembodiments, a single locator having three sensors may be used tosimultaneously collect the magnetic field measurements. In otherembodiments, a locator having one magnetic field sensor may collectmagnetic field measurements at multiple positions. The positioninformation may be determined by, for example, a position sensingmodule, such as module 912 as shown in FIG. 9, or by other positionsensing methods, such as based on predetermined offsets, mechanical orelectrical position determination mechanisms, or by other positionsensing methods.

At stage 1020, the received magnetic field signals at three or morepositions may be processed, such as by use of a processor element suchas element 940 of FIG. 9 in conjunction with memory 945, in accordancewith a sheet current flow model approximation, to determine an estimateddistance/depth to a buried object. The sheet current flow model mayinclude two or more magnetic field components, which may include a sheetcurrent approximation magnetic field component and a conductor currentapproximation magnetic field component. For example, the sheet currentapproximation may be based on an infinite sheet current, resulting in aconstant term, and the conductor current approximation may be based on acurrent flowing in a straight conductor. Other sheet current flow modelsmay be used, such as, for example, a model including a non-infinitecurrent sheet, which may vary as a function of distance relative to theburied object. In addition, the conductor current approximation may bebased on a sonde magnetic field model, or other conductor currentmagnetic field model different from the magnetic field model associatedwith an infinite straight conductor approximation. Additional positionalinformation may be provided and used, such as location informationprovided from inertial, compass, and/or GPS devices, to further enhancethe distance estimate.

Additional processing, such as to adjust for translation positions,determine estimates of magnetic field at virtual positions, determinedepth based on a rotational offset from a centerline, and/or otheradjustments may be further performed to determine the distance estimate.

At stage 1030, the distance estimate may be saved to a memory and/oroutput, such as on a storage device such as a USB thumb drive, and/ormay be displayed on a user interface device, such as an LCD display, asaudio output, as text-based output, and the like. In some embodiments,the buried object information may be combined with the positioninformation and mapping information to provide data and/or maps ofburied object depths, locations, etc., combined with locationinformation.

In an exemplary embodiment, a closed form solution of the distancedetermination process may be implemented, such as in processing element940 and in conjunction with memory module 945, to efficiently solve forthe distance/depth estimate to the buried object. Alternately, or inaddition, open form solutions, such as iterative solutions, numericalapproximations, and/or other non-closed form solutions may beimplemented to determine the depth estimate.

FIG. 11 illustrates details of another process embodiment 1100 fordetermining a depth estimate to a buried object based on threemeasurements taken either simultaneously using three or more sensorelements or sequentially using one or two sensor elements. Process 1100may be implemented in a three sensor locator, such as those shown inFIG. 1 or 6, and implemented in processing circuitry such as shown inFIG. 9. At stage 1110, magnetic field signals emitted from the buriedobject may be measured. In an exemplary embodiment, the measurements aretaken at non-uniformly spaced positions substantially along a verticalline intersecting the buried object, however, the measurements may, insome embodiments, be taken at uniformly spaced positions and/or offsetfrom vertical as described with respect to FIGS. 7 and 8. If the locatoris initially positioned on the ground H may be determined based on theknown distance from the bottom of the locator to a reference position,such as the sphere radius if the lower sensor is a spherical magneticfield sensor. Alternately, distance information may be provided from aseparate distance sensor element.

At stage 1120, the three magnetic field measurements and associateddistance measurements may be processed using a closed form sheet currentflow model of the form of equation (1) as described previously herein,where the depth estimate, D_(b), is determined as:

$D_{b} = {\frac{( {{- B_{m}} + B_{t}} )*{sep}_{1}*{sep}_{2}}{{- ( {B_{t}*{sep}_{1}} )} + {B_{b}*( {{sep}_{1} - {sep}_{2}} )} + {B_{m}*{sep}_{2}}} - H}$

At stage 1130, the depth estimate may be stored in a memory of thelocator and/or sent to an external electronic computing system. At stage1130, a visual display of the depth estimate may be provided on adisplay device of the locator, such as in a graphic user interface (GUI)display in a graphic and/or numeric format.

FIG. 12 illustrates an example embodiment 1200 of processing magneticfield measurements and generating associated distance information usingan accelerometer element 1230 in a buried object locator to determine anestimated depth to a buried object 1250. The accelerometer 1230 may bedisposed on or within a magnetic sensor assembly 1210 mast or sensorelement, or elsewhere on or in the locator (not shown). In theembodiment shown in FIG. 12, the accelerometer is positioned near asensor 1211. In operation, at Stage 1, a user may bump or tap thelocator onto the ground. The accelerometer 1230 may generate an outputsignal that when processed, such as in a processing element of thelocator, can be used to detect that the locator is at the lowest orground position. Alternately, or in addition, the accelerometer or otherdistance measurement element may be initiated or triggered by a user atthe ground or other reference position.

At Stages 2 through 4, the locator may be raised by the operator tosuccessive heights above the ground H₁, H₂, and H₃ as shown, withmeasurements taken at corresponding positions P₁, P₂, and P₃. P₁ mayalso be at the ground point or a known offset from the ground (e.g., thesensor ball radius) rather than at a first raised point as shown. Thedistances between positions P₁, P₂, and P₃ and the ground surface may bedetermined by double-integrating the accelerometer output (in thevertical direction or Z-axis). Additional measurements and associateddistances may be taken at other positions and stages (not shown), suchas at higher distances above the ground and/or at positions intermediateto those previously taken. The measurement triggering may be done by auser in some embodiments and/or may be done automatically by the locatorbased on sensed distances from the accelerometer outputs and/or based onpredefined time intervals or other measurement parameters.

FIG. 13 illustrates another locator embodiment using a distance sensorelement, 1330, which may be part of a distance sensing module fordetermining the distance from a reference point on the locator to theground or other surface in a locator 1300 having two magnetic fieldsensors 1311 and 1312 (other locator configurations, such as locatorswith one sensor or three sensors, can be similarly configured with adistance measuring element). Distance sensor element 1330 may be, forexample, an infra-red distance sensor, acoustic distance sensor, imagingdistance sensor, electromechanical distance sensor, or other distancesensor device as known or developed in the art to determine a distance,D_(DS), to the ground 180 surface. The distance sensor measurements canbe used in processing as described previously herein, such as in locatorcontrol, processing, and display module 1320, to determine buried object1350 depth, D_(b), by providing distance information associated withmagnetic field measurements taken by the locator. For example, thedistance sensor 1330 will be at a known distance offset, D_(OFF), from asensor element 1311, and the corresponding height of the sensor element1311 above the ground, H, can be determined by subtracting D_(OFF) fromD_(DS). Processing can be performed using a sheet current flow model,such as the three measurement or four measurement sheet current modelsolutions described previously herein, to determine an estimate ofburied object depth D_(b).

FIG. 14 illustrates details of an embodiment 1400 of a process fordetermining a depth estimate of a buried object below a ground surface.Process 1400 may be implemented on a locator device such as locatorembodiment 1300 of FIG. 13 or locator embodiment 1400 of FIG. 14.Process 1400 may be implemented in a locator circuit configuration suchas shown in locator embodiment 900 of FIG. 9.

Process 1400 may begin at stage 1410, where magnetic field measurementsmay be taken at an initial three positions. In addition, a measurementof distance from a reference point on the locator to the ground surfacemay be taken at each magnetic field measurement position and associatedwith the magnetic field measurements. This combination of magnetic fieldmeasurements and associated distance measurements may then be used togenerate a first depth estimate at stage 1415 using a sheet current flowmodel as described previously herein, which may then be stored inmemory.

The magnetic field measurement and distance measurement process may thenbe repeated to generate additional depth estimates, where eachadditional depth estimate may be based on at least one differentmagnetic field and distance measurement (as compared to the other depthestimates). For example, at stage 1420, another magnetic field anddistance measurement may be taken at another position and stored inmemory. Based on this additional measurement set, another depth estimatemay be determined. For example, if the measurements taken at stage 1415consist of measurement sets M1, M2, and M3 (where Mn corresponds with amagnetic field and distance pair taken at position n), a new measurementpair, M4, may be taken at position 4 and a depth estimate may bedetermined based on measurement pairs M2, M3, and M4. Other permutationsof measurement pairs may also be used in some embodiments. For example,a second depth estimate may be based on M4, M5, and M6, where additionalmeasurements are taken at subsequent positions 5 and 6. At stage 1425,the additional depth estimate may be generated, such as by using thesheet current flow models described previously herein, and stored inmemory.

To improve the overall depth estimate, these first, second, and/oradditional depth measurements may be averaged, either equally or basedon a weighted average, to generate an aggregate depth estimate. Thenumber of depth estimates used to generate the aggregate may bedetermined at decision stage 1430, where a decision may be made as towhether a desired number of estimates for use in the aggregate have beencollected. If they have not, processing may return to stage 1420, whereadditional measurements and depth estimates may be made. Alternately, ifa desired number of depth estimates have been determined, (e.g., 2, 3,or more) processing may proceed to stage 1440 where the aggregate depthestimate may be determined by averaging the previously determinedplurality of depth estimates. At stage 1450, the aggregate/averageddepth estimate may be displayed on a display element of the locatorand/or stored in a memory of the locator, and/or sent to an externalcomputing system for further display, review, storage, and/orprocessing.

In some configurations, the apparatus or systems described herein mayinclude means for implementing features or providing functions relatedto buried object depth estimation as described herein. In one aspect,the aforementioned means may be a module including a processor orprocessors, associated memory and/or other electronics in whichembodiments of the disclosure reside, such as to implement buried objectdepth location functions as described herein. These may be, for example,modules or apparatus residing in buried locators or other systems suchas computer systems, mobile phones, server systems, or other electronicor computing systems.

In one or more exemplary embodiments, the electronic functions, methodsand processes described herein and associated with buried objectdetection functions may be implemented in hardware, software, firmware,or any combination thereof. If implemented in software, the functionsmay be stored on or encoded as one or more instructions or code on acomputer-readable medium. Computer-readable media includes computerstorage media. Storage media may be any available media that can beaccessed by a computer. By way of example, and not limitation, suchcomputer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or otheroptical disk storage, magnetic disk storage or other magnetic storagedevices, or any other medium that can be used to carry or store desiredprogram code in the form of instructions or data structures and that canbe accessed by a computer. Disk and disc, as used herein, includescompact disc (CD), laser disc, optical disc, digital versatile disc(DVD), floppy disk and blu-ray disc where disks usually reproduce datamagnetically, while discs reproduce data optically with lasers.Combinations of the above should also be included within the scope ofcomputer-readable media.

As used herein, computer program products comprising computer-readablemedia including all forms of computer-readable medium except, to theextent that such media is deemed to be non-statutory, transitorypropagating signals.

It is understood that the specific order or hierarchy of steps or stagesin the processes and methods disclosed herein are examples of exemplaryapproaches. Based upon design preferences, it is understood that thespecific order or hierarchy of steps in the processes may be rearrangedwhile remaining within the scope of the present disclosure.

Those of skill in the art would understand that information and signals,such as video and/or audio signals or data, control signals, or othersignals or data may be represented using any of a variety of differenttechnologies and techniques. For example, data, instructions, commands,information, signals, bits, symbols, and chips that may be referencedthroughout the above description may be represented by voltages,currents, electromagnetic waves, magnetic fields or particles, opticalfields or particles, or any combination thereof.

Those of skill would further appreciate that the various illustrativelogical blocks, modules, circuits, and algorithm steps described inconnection with the embodiments disclosed herein may be implemented inone or more processing elements comprising electronic hardware, computersoftware, electro-mechanical components, or combinations thereof.Whether such functionality is implemented as hardware or softwaredepends upon the particular application and design constraints imposedon the overall system. Skilled artisans may implement the describedfunctionality in varying ways for each particular application, but suchimplementation decisions should not be interpreted as causing adeparture from the scope of the present disclosure.

The various illustrative functions and circuits described in connectionwith the embodiments disclosed herein with respect to locator systemsmay be implemented or performed in a processing element including ageneral purpose processor, a digital signal processor (DSP), anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA) or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions described herein. A generalpurpose processor may be a microprocessor, but in the alternative, theprocessor may be any conventional processor, controller,microcontroller, or state machine. A processor may also be implementedas a combination of computing devices, e.g., a combination of a DSP anda microprocessor, a plurality of microprocessors, one or moremicroprocessors in conjunction with a DSP core, or any other suchconfiguration.

The steps or stages of a method, process or algorithm described inconnection with the embodiments disclosed herein may be embodieddirectly in hardware, in a software module executed by a processor, orin a combination of the two. A software module may reside in RAM memory,flash memory, ROM memory, EPROM memory, EEPROM memory, registers, harddisk, a removable disk, a CD-ROM, or any other form of storage mediumknown in the art. An exemplary storage medium is coupled to theprocessor such that the processor can read information from, and writeinformation to, the storage medium. In the alternative, the storagemedium may be integral to the processor. The processor and the storagemedium may reside in an ASIC. The ASIC may reside in a user terminal. Inthe alternative, the processor and the storage medium may reside asdiscrete components in a user terminal.

The disclosure is not intended to be limited to the aspects shownherein, but is to be accorded the full scope consistent with thespecification and drawings, wherein reference to an element in thesingular is not intended to mean “one and only one” unless specificallyso stated, but rather “one or more.” Unless specifically statedotherwise, the term “some” refers to one or more. A phrase referring to“at least one of” a list of items refers to any combination of thoseitems, including single members. As an example, “at least one of: a, b,or c” is intended to cover: a; b; c; a and b; a and c; b and c; and a, band c.

The previous description of the disclosed aspects is provided to enableany person skilled in the art to make or use the present disclosure.Various modifications to these aspects will be readily apparent to thoseskilled in the art, and the generic principles defined herein may beapplied to other aspects without departing from the spirit or scope ofthe disclosure. Thus, the presently claimed invention is not intended tobe limited to the aspects shown herein but is to be accorded the widestscope consistent following claims and their equivalents.

I claim:
 1. A method for locating a buried object with a buried objectlocator, comprising: generating, in the buried object locator, a firstmagnetic field measurement at a first position; generating, in theburied object locator, a second magnetic field measurement at a secondposition different from the first position; generating, in the buriedobject locator, a third magnetic field measurement at a third positiondifferent from the first and second positions storing the first, second,and third magnetic field measurements and associated positioninformation in a non-transitory memory of the locator; processing thefirst, second, and third magnetic field measurements and associatedposition information in accordance with a closed-form sheet current flowmodel to generate an estimate of the depth, Db, of the buried objectbelow a ground surface, wherein the sheet current flow model includes amagnetic field component modeled as being generated by an infinite sheetcurrent and another magnetic field component modeled as being generatedby a current flowing in a buried conductor in the form:${D_{b} = {\frac{( {{- B_{m}} + B_{t}} )*{sep}_{1}*{sep}_{2}}{{- ( {B_{t}*{sep}_{1}} )} + {B_{b}*( {{sep}_{1} - {sep}_{2}} )} + {B_{m}*{sep}_{2}}} - H}};$and storing the estimate of the depth in the non-transitory memory ofthe locator for either providing an estimate of the depth to a user ofthe buried object locator, post-processing of the estimated depth, orboth.
 2. The method of claim 1, wherein the first, second, and thirdpositions are approximately co-linear on a line intersecting the buriedobject.
 3. The method of claim 2, wherein the line is along a verticalcenterline extending upward from the buried object and ground surface.4. The method of claim 2, wherein the line is offset at an angle ofapproximately ten degrees or less from a vertical centerline extendingupward from the buried object and ground surface.
 5. The method of claim1, wherein the first, second, and third positions are co-linear on aline translated horizontally from a vertical centerline extending upwardfrom the buried object and ground surface.
 6. The method of claim 1,wherein the measurements at the first, second, and third positions aregenerated by corresponding first, second, and third magnetic fieldantenna sensors.
 7. The method of claim 6, wherein the measurements atthe first, second, and third positions are generated approximatelysimultaneously by the first, second, and third magnetic field antennasensors.
 8. The method of claim 1, wherein the measurements at thefirst, second, and third positions are generated sequentially by asingle magnetic field antenna sensor moved between the first, second,and third positions.
 9. The method of claim 1, wherein the measurementsat the first, second, and third positions are generated by two magneticfield antenna sensors moved between two or more of the positions. 10.The method of claim 1, wherein the first and second positions are at afirst distance relative to each other and the second and third positionsare at a second distance relative to each other, wherein the firstdistance is different than the second distance.
 11. The method of claim1, further comprising: automatically determining an optimal measurementposition above the ground to the buried object; generating andprocessing the magnetic field measurements responsive to theautomatically determining an optimal measurement position.
 12. Themethod of claim 11, wherein the automatically determining an optimalmeasurement position above the ground includes determining a centerlineusing one or more horizontally oriented magnetic field sensors toprovide information to position the locator over the buried object. 13.The method of claim 1, further comprising: storing a specification of aburied object depth in the locator; comparing the estimated depth to thespecification depth; and providing, responsive to the comparing, anotification.
 14. The method of claim 13, wherein the notificationincludes providing an operator alarm if the estimated depth is less thanthe specification.
 15. The method of claim 13, wherein the notificationincludes storing a database entry indicative of the difference betweenthe estimated depth and the specification.
 16. The method of claim 1,wherein the estimate of the depth is provided on a visual display of thelocator.
 17. A locator for determining the location of a buried object,comprising: A housing; A magnetic field sensor assembly including: oneor more magnetic field sensors configured to generate first, second, andthird magnetic field measurement information at corresponding first,second, and third positions; a non-transitory memory module; and aprocessor module disposed in the housing and operatively coupled to thenon-transitory memory module, wherein the processor is programmed to:receive the first, second, and third magnetic field measurementinformation from the magnetic field sensor(s); process the receivedfirst, second, and third magnetic field measurement information inaccordance with a closed-form sheet current flow model to generate anestimated distance to the buried object, wherein the sheet current flowmodel includes a magnetic field component modeled as being generated byan infinite sheet current and another magnetic field component modeledas being generated by a current flowing in a buried conductor in theform:$D_{b} = {\frac{( {{- B_{m}} + B_{t}} )*{sep}_{1}*{sep}_{2}}{{- ( {B_{t}*{sep}_{1}} )} + {B_{b}*( {{sep}_{1} - {sep}_{2}} )} + {B_{m}*{sep}_{2}}} - H}$determine an estimated depth of the buried object based on the distance;and store the estimated depth in the non-transitory memory of thelocator for either providing the estimated depth to a user of thelocator, post-processing of the estimated depth, or both.
 18. Thelocator of claim 17, wherein the magnetic field sensor assemblyincludes: a first magnetic field sensor module configured to generatethe first magnetic field measurement information; a second magneticfield sensor module configured to generate the second magnetic fieldmeasurement information; and a third magnetic field sensor moduleconfigured to generate the third magnetic field measurement information.19. The locator of claim 17, wherein the magnetic field sensor assemblyincludes: a location determination module; and A magnetic field sensormodule configured to generate the first magnetic field measurementinformation, the second magnetic field measurement information, and thethird magnetic field measurement information based at least in part oninformation provided from the location determination module.